Maths Olympiad
Exam
Find all real numbers a for which the equation
x^2 + (a + 2)x + 1 = 3|x| has exactly three distinct real solutions in x.
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Maths Olympiad Other Question
Suppose P is an interior point of a triangle ABC such that the ratios
d(A,BC)
d(P,BC)
,
d(B,CA)
d(P,CA)
,
d(C,AB)
d(P,AB)
Let ABC be a triangle. Let D, E, F be points respectively on the segments BC, CA, AB such that AD, BE, CF concur at the point K. Suppose BD/DC = BF/FA and ADB = AFC. Prove that ABE = CAD